论文标题
级代数与循环型希尔伯特系列
Graded algebras with cyclotomic Hilbert series
论文作者
论文摘要
让$ r $成为一个在田野上的积极分级代数。我们说，如果其减少的希尔伯特系列的分子在单位圈子上的所有根源，则$ r $是希尔伯特 - 循环的。这种环自然出现在交换代数，数值半群理论和Ehrhart理论中。如果$ r $是标准分级，我们证明，在额外的假设中，$ r $是koszul或具有不可还原的$ h $ polynomial，hilbert-cyclotomic代数与完全交叉点相吻合。在Koszul情况下，这是一些经典结果，该结果是关于分级代数偏差的消失。
Let $R$ be a positively graded algebra over a field. We say that $R$ is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. Such rings arise naturally in commutative algebra, numerical semigroup theory and Ehrhart theory. If $R$ is standard graded, we prove that, under the additional hypothesis that $R$ is Koszul or has an irreducible $h$-polynomial, Hilbert-cyclotomic algebras coincide with complete intersections. In the Koszul case, this is a consequence of some classical results about the vanishing of deviations of a graded algebra.
